Similate a vessel being filled with a liquid
If you just want to raise the liqud level, you can have the inner shape with a volumetric material sat up as water and then make a cube and add wave modifier to it. Then add a boolean modifier to ineract with the inner shape of the Vessel. Then animate the cube to rise up in Z direction. (The inner shape of the vessel must be seperated object from the vessel) Also I suggest to retopology the mesh, it seems that there are some n-gons in your mesh that are causing some shadowing problems or could be wrong sided normals...